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Problem solution · Java

Find the Maximum Number of Elements in Subset

Find the Maximum Number of Elements in Subset: a Java solution using hash-based lookup. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Hash-based lookup
Source
walkccc LeetCode Solutions
Length
30 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Hash-based lookup

For Find the Maximum Number of Elements in Subset, the implementation stores previously seen values or frequencies in a hash table for direct membership and lookup operations.

  1. Decide the key that represents the information needed later.
  2. Update its count or stored state while scanning the input.
  3. Use constant-time expected lookups to detect matches or assemble the result.

Code notes

  • 30 lines of Java from the credited upstream file 3020.java.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • 3 loop blocks detected.

Complexity

Expected hash operations are constant time, but the surrounding scan and the number of stored keys determine total work and memory.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeFind the Maximum Number of Elements in Subset · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int maximumLength(int[] nums) {    final int maxNum = Arrays.stream(nums).max().getAsInt();    Map<Integer, Integer> count = new HashMap<>();     for (final int num : nums)      count.merge(num, 1, Integer::sum);     int ans = count.containsKey(1) ? count.get(1) - (count.get(1) % 2 == 0 ? 1 : 0) : 1;     for (final int num : nums) {      if (num == 1)        continue;      int length = 0;      long x = num;      while (x <= maxNum && count.containsKey((int) x) && count.get((int) x) >= 2) {        length += 2;        x *= x;      }      // x is now x^k, and the pattern is [x, ..., x^(k/2), x^(k/2), ..., x].      // The goal is to determine if we can insert x^k in the middle of the      // pattern to increase the length by 1. If not, we make x^(k/2) the middle      // and decrease the length by 1.      ans = Math.max(ans, length + (count.containsKey((int) x) ? 1 : -1));    }     return ans;  }}

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